Ultrasonic Location

Idea: two or more active chirp boards and a homebase. All boards have
both an rf and an ultrasonic transceiver, and a unique ID. Homebase
sends an rf signal "Board 1 chirp." Upon receipt of signal, Board 1
chirps, all others start timer, listen, and wait for Board 1's chirp
to arrive. When it does, they stop timer, and send time-of-flight to
Homebase. This gives you distance from Board 1 to all other boards.
Repeat for Board 2...Board N, and get a full distance matrix, which
Homebase can solve for relative location of each using least-squares
or whatever they use for GPS these days.

Echoes are not a problem (as in ultrasonic distance sensing) because
you are only interested in the first-arriving acoustic signal (echoes
will come later). Zigbee may be problematic as latency is unknown...
but could be experimentally determined; if it's consistent or at least
predictable it would work, or could use cheap 900 mHz transceivers.

Contents

Algorithm

I sat down and solved the 2-D position from distance. (This turns out
to actually be harder than the GPS problem because satellites know
where they are, and the only unknowns are the single GPS receiver
position and clock skew.) For three points you can do it closed-form,
but note that that's six unknowns (x and y for three points A, B, C)
from only three distances d(AB), d(AC), and d(BC). So you have to
assume a fixed translation (say, Ax = Ay= 0)) and rotation (say, Bx =
0) This makes an argument for a fixed base station, because otherwise
we can't detect when the whole fleet moves in the same direction. And
we probably want another fixed base station to keep the fleet rotation
from drifting. But that could be as simple as just two sensor boards
on poles (which would be as robust -- or not -- as robot-mounted
ones).

Acoustics

Re acoustics, as I understand it ultrasonic transceivers have a pretty
narrow resonance around 40 kHz and all you do is hit them with a
approx 10-15 VRMS square wave at that frequency. (I'm not sure how
well you can modulate them -- at least the cheap ones -- because they
will ring for a ms or two.) I've heard of people using max232s to get
a nice beefy drive voltage on the cheap. On the receiver end my first
hack would be to XOR the received signal down to baseband from the
local driver frequency rather than using fancy bandpass analog filters
or DSP. It will be worth checking out some ultrasonic distance sensor
schematics and see what we can steal, um, what inspires us.

RF

The nRF24L01 Single Chip 2.4GHz Transceiver is something to look at as an alternative to Zigbee

Previous Work

There's no obvious reason this wouldn't work. I've seen a working
proof-of-concept with Olivetti research "bats" location sensing (fixed
recievers, mobile transmitter).